Determine the effect of changing the reference frame (including the origin) on t

Question

Determine the effect of changing the reference frame (including the origin) on the fol lowing quantities: a. The position and displacement vector dr. (2 pts) b. The velocity and acceleration ã. (2 pts) c. The relative mass; For the two-body system of sub-components m and m2, the relative mass is defined as mr =. (2 pts) d. The momentum and angular momentum L of a particle. (2 pts e. The equation of motion, F = and torque-d of a single particle. (3/4 pts) f. Repeat e) for a system of N particles with a mass mi &i1; . N. (4/5 pts) 72 dt'

Explanation / Answer

a. The position "r" will change as it is measured with respect to the origin whereas "dr" will not change it is a difference between two points which would be the same irrespective of the reference frame.

b. The velocity "v" will not change because it is defined as "dr/dt", so as "dr" will not change, hence "v" will not change and same goes for "a", as "a" is "dv/dt", "a " will also not change.

c. Relative mass is independent of coordinates, hence will not change.

d. The momentum will not change as it is just product of m*(dv/dt), and "dv" doesn't change, so "p" doesn't change but the angular momentum "L" will change as it is defined as m*v*r, and as we saw earlier that "r" changes, so "L" would change too.

e. Using similar logics as in d. "F" wouldn't change and "tau" would change.

f. The result would stay the same.

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